1. Field of the Invention
The present invention relates generally to geological formation evaluation techniques. The invention further relates to the interpretation of electrical resistivity measurements to evaluate fluid content. More particularly, the present invention relates to the evaluation of water and hydrocarbon saturation in shaly-sand formation and other formations from resistivity and porosity values.
2. Background
A common method for evaluating the hydrocarbon content of reservoirs entails the use of electrical resistivity measurements. In accordance with known interpretation techniques, one or more types of porosity-related measurements is combined with measurements of electrical resistivity, R (or its inverse, electrical conductivity, C) to infer the character of the fluid content within the pore spaces of the formation. The fractional volumes of connate water and hydrocarbons in the formation may be obtained from empirical relationships between total formation resistivity Rt and porosity and connate water resistivity. One such relationship, called the “Archie relationship” or “Archie Equation” is universally applied in fluid reservoir calculations to obtain an estimate of water saturation from wireline logs in shale-free formations. See e.g. Archie, “The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics”, Transactions AIME, 146 (1942), p. 54-62.
The Archie equation provides an estimate of total water saturation Sw by combining reservoir properties of porosity, water conductivity, and total conductivity along with parameters a, m, and n. This relationship is generally used to evaluate the fractional volume, Sw, of porosity that is filled with formation water. The potential of a zone in the formation to produce hydrocarbons is often measured in terms of water saturation, Sw. Given this fractional volume, the remaining fractional amount So is assumed to be occupied by hydrocarbons.
In the Archie relationship, water saturation Sw is provided by the following expression:
                              S          w          n                =                                            R              0                                      R              t                                =                                    1                              R                t                                      ·                                          aR                w                                            Φ                m                                                                        (        1        )            or as:
                              S          w          n                =                              C            t                                              Φ              m                        ·                          C              w                                                          (        2        )            where,                Sw=formation water saturation, fraction,        Ct=rock conductivity, mho/m,        Cw=brine conductivity, mho/m,        Rw=resistivity of formation water, ohm-m,        Rt=resistivity of formation rock, ohm-m,        Φ=porosity, fraction,        n=saturation exponent, and        m=cementation exponent.        
The constants n and m are empirically determined values that relate porosity (represented by Φ) to resistivity, Ro, of porous rock formation that is completely saturated with water, Ro. The values for n and m are typically estimated from core data analysis or are known through past experience with the formation in question. The formation resistivity, Rw, represents the resistivity of the formation water disposed in the pore spaces of the formation. Formation water resistivity may be obtained from field measurements and/or log analysis estimation. On the other hand, values for formation rock resistivity Rt is typically obtained from deep resistivity log readings. Porosity values may be estimated from porosity logs such as density, neutron or sonic logs.
The accuracy of estimates of total water saturation derived from the Archie Equation begins to fall, when the estimate is applied for a shaly-sand formation. Shaly-sand formation includes clay minerals and clay components that retain water. This highly conductive water increases the value of the conductivity measurements, while decreasing the resistivity measurements. The Archie equation assumes, however, that the formation water is the only source of conductivity in the formation. If uncorrected resistivity values are used in the Archie equation and other conventional calculations, an overestimation of water saturation results and the presence of hydrocarbon content may be overlooked.
Accordingly, expansions of the Archie equation have been developed to account for the conductivity effect of water associated with clay minerals and components in shale, thereby providing a more accurate evaluation of water saturation. The “dual water equation” or “dual water method”, and similar models, were introduced for this purpose (see, e.g., Clavier et al., “The Theory and Experimental Bases for the ‘Dual Water’ Model of the Interpretation of Shaly Sands”, SPE 6859, 1977, pp. 3-18 (hereby incorporated by reference for all purposes and made a part of the present disclosure)).
The Dual Water Models take into account an ionic double-layer in the clay components of shaly sand stones. According to this model, clay platelets are negatively charged as the result of ion substitutions in the lattice and broken bonds at the edge. Sodium cations (Na+) are held in suspension close to the clay surface when the clay is in contact with saline solution and act as charge-balancing cations. As a result, Cl-anions in the saline solution are repelled from the clay surface. Further, a mono-layer of adsorbed water forms on the clay surface and is joined by a layer of hydrated Na+ ions. This layer acts to further balance the negative charge of the clay platelets. Measured in terms of cation exchange capacity (CEC), the concentration of Na+ ions provide an additional source of conductivity.
Following the above observation, Waxman and Smits proposed an empirically-derived saturation-resistivity relationship to calculate the fractional volume of pore space capable of holding producible hydrocarbons. This relationship assumes that cation conduction and the conduction of normal sodium chloride act independently in the pore space, resulting in parallel conduction paths. See e.g., M. H. Waxman, et al. “Electrical Conductivities in Oil Bearing Shale Sands,” SPE Journal, vol. 8, no. 2, Society of Petroleum Engineers, (1968). This model can be expressed by the following Waxman-Smits equation:
                              C          t                =                                                            S                w                n                            ·              Cw                                      F              *                                +                                    B              ·                              Q                v                            ·                              S                w                                  n                  -                  1                                                                    F              *                                                          (        3        )            where,                Ct=rock conductivity,        Sw=water saturation,        n=saturation exponent for shaly formations,        B=equivalent conductance of clay counterions,        Qv=cation exchange capacity per unit pore volume,        Cw=water conductivity, and        F*=formation factor of the interconnected porosity.        
Under the Waxman-Smits model, an assumption is made that shaly formation behaves like a clean, shale-free formation of the same porosity, tortuosity, and fluid saturation, except that the water appears to be more conductive than its bulk salinity. The increase of apparent water conductivity is dependent on the presence of counter-ion.
The Dual Water equation modifies the Waxman-Smits equation by taking into account the exclusion of anions from the double-layer. (See e.g., Kurniawon, Fnu, “Evaluation of the Hydrocarbon Potential in Low-Salinity Shaly Sand.” Louisiana State University, Masters' Thesis; Apr. 4, 2002). The Dual Water model represents the counterion conductivity restricted to the clay bound water, where counterion reside, and to the free water, which is found at a distance away from the clay surface. Id. This model provides that apparent water conductivity depends on the relative volumes of clay bound water and free water. The dual water model correctly assumes that irreducible water and free or mobile water have the same conductivity and considers the two volumes together as a single volume.
In the dual water equation, water saturation Sw is expressed as follows:
                                          Sw            =                          swb              ·                                                (                                      cwf                    -                    cbw                                    )                                                  2                  ·                  cwf                                                                               +                                         [                                                                                                                                                              4                        ⁢                                                                                                  ⁢                                                  cudc                          ·                          cwf                          ·                                                      phit                            mDwa                                                                                              +                                                                        (                                                                                    (                                                              cwf                                -                                cbw                                                            )                                                        +                                                          swb                              ·                                                              phit                                mDwa                                                                                                              )                                                2                                                                                                  2                    ⁢                                                                                  ⁢                                          cwf                      ·                                              phit                        mDwa                                                                                            ]                                                                        (        4        )            where,                Swb=fractional portion of total porosity saturated with clay bound water,        Cwf=conductivity of freely moving water,        Cbw=conductivity of clay bound water,        cudc=deep conductivity,        phit=total porosity, and        m Dwa=cementation exponent.        